where \(\kappa \)  is the region of support of \(c_m\)  such that \(\sum _{m\in \kappa } c_m^2 \cong E\)  and the \(\sum _k k \beta _k\)  term loosely approximates the M-GBF's region of support [1]}. Note that the \(E\)  term in front of the M-GBF argument ensures proper scaling with \(c_m^2\)  since \(\sum _m c_m^2 = E\)  and \(\sum _m |\mathcal {I}_m^{1:K}\left(\lbrace -j\beta _k\rbrace \right)|^2 = 1\)  [1]}. The quartic objective function defined in (REF ) is loosely similar to those defined in other generalized phase retrieval problems [3]}, [4]}. The quartic nature of this distance metric between \(c_m^2\)  and \(|\mathcal {I}_m^{1:K}\left(\lbrace -j\beta _k\rbrace \right)|^2\)  coupled with the highly oscillatory nature of the M-GBFs with varying arguments make the objective function defined in (REF ) nonconvex. Such an objective function makes it unlikely that common iterative methods will solve this problem without special consideration to initialization. However, efforts in the literature [5]}, [6]} have demonstrated that heuristic methods work surprisingly well on these nonconvex problems and produce useful results.
